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Galaxies located in the environment or on the line of sight towardsgravitational lenses can significantly affect lensing observables, and can leadto systematic errors on the measurement of $H_0$ from the time-delay technique.We present the results of a systematic spectroscopic identification of thegalaxies in the field of view of the lensed quasar HE0435-1223, using the W. M.Keck, Gemini and ESO-Very Large telescopes. Our new catalog triples the numberof known galaxy redshifts in the vicinity of the lens, expanding to 102 thenumber of measured redshifts for galaxies separated by less than 3 arcmin fromthe lens. We complement our catalog with literature data to gather redshifts upto 15 arcmin from the lens, and search for galaxy groups or clusters projectedtowards HE0435-1223. We confirm that the lens is a member of a small group thatincludes at least 12 galaxies, and find 8 other group candidates near the lineof sight of the lens. The flexion shift, namely the shift of lensed imagesproduced by high order perturbation of the lens potential, is calculated foreach galaxy/group and used to identify which objects produce the largestperturbation of the lens potential. This analysis demonstrates that i) at mostthree of the five brightest galaxies projected within 12 arcsec of the lensneed to be explicitly used in the lens models, and ii) the groups can betreated in the lens model as an external tidal field (shear) contribution.

H0LiCOW II. Spectroscopic survey and galaxy-group identification of the strong gravitational lens system HE0435-1223